A finite time anti-disturbance control method for a universal pneumatic flexible manipulator

Abstract

A finite-time anti-interference control method for a universal pneumatic flexible manipulator includes the following steps: The universal pneumatic flexible manipulator is simplified to a link model using the D-H method, and kinematic analysis is performed to obtain the kinematic analysis model and the position of the end point of the universal pneumatic flexible manipulator; based on the kinematic analysis model of the universal pneumatic flexible manipulator, a dynamic model of the universal pneumatic flexible manipulator is established using the Euler-Lagrange method; the uncertainty of the universal pneumatic flexible manipulator is considered as a disturbance, and a second-order mathematical model of the pneumatic flexible manipulator is established; a finite-time extended state observer is designed to estimate the disturbance, and based on the disturbance estimate, a finite-time backstepping controller is designed to compensate for the influence of the disturbance on the system; to address the model uncertainty, a finite-time control method is designed to compensate for the influence on the position control accuracy of the pneumatic flexible manipulator, exhibiting strong robustness and high control accuracy.

Description

Technical fields:

[0001] This invention belongs to the fields of pneumatic servo systems and anti-interference control, specifically relating to a finite-time anti-interference control method for a universal pneumatic flexible robotic arm. Background technology:

[0002] With the rapid development of robotics technology, robotic arms are widely used in the field of intelligent manufacturing. To meet the requirements of intelligent manufacturing sites for the compliance and flexibility of robotic arms, a pneumatic flexible robotic arm driven by pneumatic artificial muscles was designed to realize functions such as grasping and handling.

[0003] The omnidirectional pneumatic flexible manipulator is a multi-degree-of-freedom linkage mechanism connected by universal joints. Establishing kinematic and dynamic models of the omnidirectional pneumatic flexible manipulator based on its structural characteristics has high research significance and value. However, the uncertainty of the model has a significant impact on the precise control of the omnidirectional pneumatic flexible manipulator. Most existing studies rarely conduct detailed modeling of the omnidirectional pneumatic flexible manipulator and consider the impact of model uncertainty on the position control of the pneumatic flexible manipulator. Therefore, the steady-state and transient performance of the system will be reduced, and the expected control effect cannot be achieved. Summary of the Invention:

[0004] This invention provides a finite-time anti-interference control method for a universal pneumatic flexible manipulator. A kinematic analysis model and a dynamic model of the universal pneumatic flexible manipulator are established. To address the uncertainty of the model, a finite-time control method is designed to compensate for its impact on the position control accuracy of the pneumatic flexible manipulator, thereby achieving accurate spatial trajectory tracking of the pneumatic flexible manipulator within a finite time.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A finite-time anti-interference control method for a universal pneumatic flexible robotic arm, characterized by comprising the following steps:

[0006] The DH method is used to simplify the omnidirectional pneumatic flexible manipulator into a linkage model, and kinematic analysis is performed to obtain the kinematic analysis model and the position of the end point of the omnidirectional pneumatic flexible manipulator.

[0007] Based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator, a dynamic model of the omnidirectional pneumatic flexible manipulator is established using the Euler-Lagrange method.

[0008] The uncertainty of the omnidirectional pneumatic flexible manipulator is considered as a disturbance, and a second-order mathematical model of the pneumatic flexible manipulator is established.

[0009] Design a finite-time extended state observer to estimate disturbances, and design a finite-time backstepping controller based on the disturbance estimates to compensate for the impact of disturbances on the system.

[0010] Preferably, the step of simplifying the omnidirectional pneumatic flexible manipulator into a linkage model using the DH method and performing kinematic analysis to obtain the kinematic analysis model and the position of the end point of the omnidirectional pneumatic flexible manipulator includes:

[0011] Using the DH method, the mechanical structure of the omnidirectional pneumatic flexible manipulator is simplified into a six-bar model. To obtain the position of the end effector of the manipulator, a transition matrix A is introduced. i ;

[0012]

[0013] Where, α i-1 It is the torsion angle of the (i-1)th link; d i θ is the offset distance of the i-th link; i It is the angle of the i-th joint; based on the transfer matrix, the transfer matrix of each link of the omnidirectional pneumatic flexible manipulator is obtained as follows:

[0014]

[0015]

[0016]

[0017] Multiplying the seven transition matrices together, the position of the robotic arm's end effector is obtained as follows:

[0018]

[0019] in,

[0020]

[0021]

[0022]

[0023] In the formula: P x (t), P y (t), P z (t) represent the coordinates of the endpoint on the X, Y, and Z axes in the spatial coordinate system, respectively. C i =cosθ i (t), S i =sinθ i (t), θ i (t) is the deflection angle of the i-th joint, where i = 1, 2, 3, 4, 5, 6, and l is the length of the robotic arm link.

[0024] Preferably, the step of establishing the dynamic model of the omnidirectional pneumatic flexible manipulator using the Euler-Lagrange method based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator includes:

[0025] The Euler-Lagrange equations can be expressed in the following form:

[0026]

[0027] Based on the Euler-Lagrange equations and kinematic analysis, the dynamic model of the omnidirectional pneumatic flexible manipulator is expressed as follows:

[0028]

[0029] In the formula: It is the inertia matrix. It is the Coriolis force matrix. This is the gravity matrix; m is the mass of the link; g is the mass of the link. T =[-g,0,0,0] is the gravitational acceleration matrix; It is the centroid distance matrix;

[0030] Among them: U pj =A1A2...QA j ...A p , U pjk =A1A2...QA j ...QA k ...A p There are three intermediate variables;

[0031]

[0032] It consists of two parameter matrices;

[0033] Based on the driving method of the omnidirectional pneumatic flexible robotic arm, the dynamic model is transformed and each element is written in vector form:

[0034]

[0035] In the formula:

[0036] U0(t)=[u1(t),u2(t),u3(t)+u4(t),u4(t)-u3(t),u5(t),u6(t)] T ,

[0037]

[0038]

[0039] Where θ(t) is the vector representation of the deflection angle, D-1 (t) is D ij The vector representation of C, C(t) is C ijk The vector representation of G, g(t) is G i The vector representation, k0 is the proportional coefficient of the electric proportional valve, u0 is the preload voltage, L0 is the original length of the pneumatic artificial muscle, R is the lever arm, b is the total length of the braided mesh, N is the number of wraps of the outer braided mesh, u i (t) is the control voltage of the i-th joint, where i = 1, 2, 3, 4, 5, 6; I6 is the identity matrix.

[0040] Preferably, the step of considering the uncertainty of the omnidirectional pneumatic flexible manipulator as a disturbance and establishing a second-order mathematical model of the pneumatic flexible manipulator includes:

[0041] Combining the kinematic analysis model and the dynamic model, the second-order mathematical model of the omnidirectional pneumatic flexible manipulator is as follows:

[0042]

[0043] In the formula,

[0044]

[0045]

[0046] in, It is D -1 The elements of (t), yes Each element, b kk (t) is The element, f k It is P x The first-order partial derivative of (t), g k It is P y The first-order partial derivative of (t), f kj It is P x The first derivative of (t), g kj It is P x The first derivative of ω(t); ω(t) represents the uncertainty of the omnidirectional pneumatic flexible robotic arm.

[0047] Preferably, the step of designing a finite-time extended state observer to estimate the disturbance and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the impact of the disturbance on the system includes:

[0048] The finite-time extended state observer is:

[0049]

[0050] In the formula,

[0051] and β1, β2 and β3 are positive adjustable parameters, and e1(t) = z1(t) - x1(t), e2(t) = z2(t) - x2(t) and e3(t) = z3(t) - x3(t) are error variables in the finite-time extended state observer;

[0052] The finite-time backstepping controller is:

[0053]

[0054] In the formula, B0 represents the system parameter; k p The parameter is positive and adjustable; the sliding surface σ1(t) is designed as follows:

[0055]

[0056] Where σ2(t) is the first derivative of σ1(t), For the backstepping method, [the variable is] a dummy variable, where [the variable is] a dummy variable. This represents the error between the sliding surface σ1(t) and 0.

[0057] In the formula, e(t) = x1(t) - v1(t) is the position error of the omnidirectional pneumatic flexible manipulator, k1, k2, k3, k4, ζ, ξ1, γ, p, and q are positive adjustable parameters, v0(t) is the desired position, and v0(t) is obtained by a tracking differentiator. Preferably, after the steps of designing a finite-time extended state observer to estimate the disturbance and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the influence of the disturbance on the system, the formula further includes: performing convergence analysis on the finite-time extended state observer using Lyapunov functions and performing convergence analysis on the finite-time backstepping controller using Lyapunov functions.

[0058] Preferably, the convergence analysis of the finite-time extended state observer using Lyapunov functions specifically includes:

[0059] We design the Lyapunov equations for a finite-time extended state observer and prove its finite-time convergence. First, we present the error system of the finite-time extended state observer as follows:

[0060]

[0061] Design proof requires relevant variables Taking its derivative, we get:

[0062]

[0063] in,

[0064]

[0065] Δ(t)=[0 0 -g(t)] T

[0066] The Lyapunov equations are designed as follows:

[0067] V(t)=ε T (t)Pε(t)

[0068] Differentiate the Lyapunov function equation V(t):

[0069]

[0070] Will λ min (P)||ε(t)|| 2 ≤V≤λ max (P)||ε(t)|| 2 Substituting into the above equation, we get:

[0071]

[0072] Convergence time satisfies:

[0073]

[0074] in:

[0075] η1∈(0,r1) and η2∈(0,r2) are two bounded constants; V(e0) is the initial value of the Lyapunov function;

[0076] Preferably, the convergence analysis of the finite-time backstepping controller using Lyapunov functions specifically includes:

[0077] Two Lyapunov functions are designed using the backstepping method. The first Lyapunov function is designed as follows:

[0078]

[0079] Differentiate V1(t) and combine have to:

[0080]

[0081] in, The error between the first derivative σ2(t) of the sliding surface and the dummy variable α1(t);

[0082] when At that time, there exists Right now Based on this, the second Lyapunov function is designed as follows:

[0083]

[0084] Taking the derivative of V2(t) and substituting it into the designed finite-time backstepping controller, we can obtain:

[0085]

[0086] Convergence time satisfies:

[0087]

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] This invention establishes a kinematic analysis model and a dynamic model of a universal pneumatic flexible manipulator. To address the uncertainty of the model, a finite-time control method is designed to compensate for its impact on the position control accuracy of the pneumatic flexible manipulator. This method has strong robustness, is easy to implement in engineering, and has high control accuracy, ensuring stable, accurate, and fast control performance. Attached image description:

[0090] Figure 1 This is a schematic diagram of a finite-time anti-interference control method for a universal pneumatic flexible robotic arm according to the present invention.

[0091] Figure 2 This is a flowchart of a preferred embodiment of a finite-time anti-interference control method for a universal pneumatic flexible robotic arm according to the present invention.

[0092] Figure 3 This is a kinematic analysis diagram of the universal pneumatic flexible robotic arm of the present invention.

[0093] Figure 4 This is a position tracking curve diagram of the universal pneumatic flexible robotic arm of the present invention.

[0094] Figure 5 This is a graph showing the estimated signal curve for state 1 of the finite-time extended state observer of the present invention. Detailed implementation method:

[0095] To clarify the technical objective of this invention and to illustrate its technical solution, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0096] Figure 1 This is a schematic diagram illustrating the principle of the method of the present invention, which explains the finite-time anti-interference control method for a universal pneumatic flexible robotic arm.

[0097] The following content combines Figure 1-4The modeling of a universal pneumatic flexible robotic arm described in this invention and the control algorithm designed to address the model uncertainty of the robotic arm are described in detail, but this is not intended to limit the invention.

[0098] A finite-time anti-interference control method for a universal pneumatic flexible robotic arm includes the following steps:

[0099] S100. Using the DH method, the universal pneumatic flexible manipulator is simplified into a linkage model, and kinematic analysis is performed to obtain the kinematic analysis model and the position of the end point of the universal pneumatic flexible manipulator.

[0100] S200. Based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator, the dynamic model of the omnidirectional pneumatic flexible manipulator is established using the Euler-Lagrange method.

[0101] S300. Consider the uncertainty of the omnidirectional pneumatic flexible manipulator as a disturbance and establish a second-order mathematical model of the pneumatic flexible manipulator.

[0102] S400. A finite-time extended state observer is designed to estimate disturbances, and based on the disturbance estimates, a finite-time backstepping controller is designed to compensate for the impact of disturbances on the system. This invention establishes the kinematic analysis model and dynamic model of a universal pneumatic flexible manipulator. To address model uncertainties, a finite-time control method is designed to compensate for their impact on the position control accuracy of the pneumatic flexible manipulator. This method exhibits strong robustness, is easy to implement in engineering, and provides high control accuracy, ensuring stable, accurate, and fast control performance.

[0103] In this embodiment, the steps of S100, simplifying the omnidirectional pneumatic flexible manipulator into a linkage model using the DH method, and performing kinematic analysis to obtain the kinematic analysis model and the position of the end point of the omnidirectional pneumatic flexible manipulator, include:

[0104] Using the DH method, the mechanical structure of the omnidirectional pneumatic flexible manipulator is simplified into a six-bar model, and the DH table is listed below:

[0105] link <![CDATA[a i ]]> <![CDATA[α i ]]> <![CDATA[d i ]]> <![CDATA[θ i ]]> 1 0 0 0 <![CDATA[θ1]]> 2 0 -90° 0 <![CDATA[θ2]]> 3 l 90° 0 <![CDATA[θ3]]> 4 0 -90° 0 <![CDATA[θ4]]> 5 l 90° 0 <![CDATA[θ5]]> 6 0 -90° 0 <![CDATA[θ6]]>

[0106] In the above formula, a i It is the length of the i-th link; α i It is the torsion angle of the i-th link; d i θ is the offset distance of the i-th link; i It is the angle of the i-th joint.

[0107] To obtain the position of the robotic arm's end effector, a transition matrix A is introduced. i ;

[0108]

[0109] Where, α i-1 It is the torsion angle of the (i-1)th link; d i θ is the offset distance of the i-th link; i This is the angle of the i-th joint; based on the DH table and the transfer matrix, the transfer matrix for each link of the omnidirectional pneumatic flexible manipulator can be obtained as follows:

[0110]

[0111]

[0112]

[0113] Multiplying the seven transition matrices together, the position of the robotic arm's end effector is obtained as follows:

[0114]

[0115] in,

[0116]

[0117]

[0118]

[0119] In the formula: P(t) is the position of the end point of the omnidirectional pneumatic flexible robotic arm, P x (t), P y (t), P z (t) represent the coordinates of the endpoint on the X, Y, and Z axes in the spatial coordinate system, respectively. C i =cosθ i (t), S i =sinθ i (t), θ i (t) is the deflection angle of the i-th joint, where i = 1, 2, 3, 4, 5, 6, and l is the length of the robotic arm link.

[0120] In this embodiment, the steps of S200, establishing the dynamic model of the omnidirectional pneumatic flexible manipulator based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator using the Euler-Lagrange method, include:

[0121] The Euler-Lagrange equations can be expressed in the following form:

[0122]

[0123] Based on the Euler-Lagrange equations and kinematic analysis, the dynamic model of the omnidirectional pneumatic flexible manipulator is expressed as follows:

[0124]

[0125] In the formula: It is the inertia matrix. It is the Coriolis force matrix. This is the gravity matrix; m is the mass of the link; g is the mass of the link. T =[-g,0,0,0] is the gravitational acceleration matrix; It is the centroid distance matrix;

[0126] Among them: U pj =A1A2...QA j ...A p , U pjk =A1A2...QA j ...QA k ...A p There are three intermediate variables;

[0127]

[0128] It consists of two parameter matrices;

[0129] Based on the driving method of the omnidirectional pneumatic flexible robotic arm, the dynamic model is transformed and each element is written in vector form:

[0130]

[0131] In the formula:

[0132] U0(t)=[u1(t),u2(t),u3(t)+u4(t),u4(t)-u3(t),u5(t),u6(t)] T ,

[0133]

[0134]

[0135] Where θ(t) is the vector representation of the deflection angle, D -1 (t) is D ij The vector representation of C, C(t) is C ijk The vector representation of G, g(t) is G i The vector representation of the electric proportional valve, where k0 is the proportional coefficient, u0 is the preload voltage, L0 is the original length of the pneumatic artificial muscle, R is the lever arm, b is the total length of the braided mesh, and N is the number of wraps of the outer braided mesh; u i (t) is the control voltage of the i-th joint, where i = 1, 2, 3, 4, 5, 6; I6 is the identity matrix.

[0136] In this embodiment, S300, the step of considering the uncertainty of the omnidirectional pneumatic flexible manipulator as a disturbance and establishing a second-order mathematical model of the pneumatic flexible manipulator includes:

[0137] Combining the kinematic analysis model and the dynamic model, the second-order mathematical model of the omnidirectional pneumatic flexible manipulator is as follows:

[0138]

[0139] In the formula,

[0140]

[0141]

[0142] in, It is D -1 The elements of (t), yes Each element, b kk (t) is The element, f k It is P x The first-order partial derivative of (t), g k It is P y The first-order partial derivative of (t), f kj It is P x The first derivative of (t), g kj It is P x The first derivative of ω(t); ω(t) represents the uncertainty of the omnidirectional pneumatic flexible manipulator. This invention establishes the kinematic analysis model and dynamic model of the omnidirectional pneumatic flexible manipulator. To address the uncertainty of the model, a finite-time control method is designed to compensate for its impact on the position control accuracy of the pneumatic flexible manipulator. This method has strong robustness, is easy to implement in engineering, and has high control accuracy, ensuring stable, accurate, and fast control performance.

[0143] In this embodiment, the steps of S400, designing a finite-time extended state observer to estimate the disturbance, and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the impact of the disturbance on the system, include:

[0144] The finite-time extended state observer is:

[0145]

[0146] In the formula,

[0147] and β1, β2 and β3 are positive adjustable parameters, and e1(t) = z1(t) - x1(t), e2(t) = z2(t) - x2(t) and e3(t) = z3(t) - x3(t) are error variables in the finite-time extended state observer;

[0148] The finite-time backstepping controller is:

[0149]

[0150] In the formula, B0 represents the system parameter; k p The parameter is positive and adjustable; the sliding surface σ1(t) is designed as follows:

[0151]

[0152] Where σ2(t) is the first derivative of σ1(t), For the backstepping method, [the variable is] a dummy variable, where [the variable is] a dummy variable. This represents the error between the sliding surface σ1(t) and 0.

[0153] In the formula, e(t) = x1(t) - v1(t) is the position error of the omnidirectional pneumatic flexible manipulator, k1, k2, k3, k4, ζ, ξ1, γ, p, and q are positive adjustable parameters, v0(t) is the desired position, and v0(t) is obtained by a tracking differentiator. Preferably, after the steps of designing a finite-time extended state observer to estimate the disturbance and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the influence of the disturbance on the system, the formula further includes: S500, performing convergence analysis on the finite-time extended state observer using a Lyapunov function and performing convergence analysis on the finite-time backstepping controller using a Lyapunov function.

[0154] In this embodiment, S501, the convergence analysis of the finite-time extended state observer is performed using the Lyapunov function, specifically including:

[0155] We design the Lyapunov equations for a finite-time extended state observer and prove its finite-time convergence. First, we present the error system of the finite-time extended state observer as follows:

[0156]

[0157] Design proof requires relevant variables Taking its derivative, we get:

[0158]

[0159] in,

[0160]

[0161] Δ(t)=[0 0 -g(t)] T

[0162] The Lyapunov equations are designed as follows:

[0163] V(t)=ε T (t)Pε(t)

[0164] Differentiate the Lyapunov function equation V(t):

[0165]

[0166] Will λ min (P)||ε(t)|| 2 ≤V≤λ max (P)|ε(t)|| 2 Substituting into the above equation, we get:

[0167]

[0168] Convergence time satisfies:

[0169]

[0170] in:

[0171] η1∈(0,r1) and η2∈(0,r2) are two bounded constants; V(e0) is the initial value of the Lyapunov function;

[0172]

[0173] Therefore, the finite-time convergence of ε(t) has been proved.

[0174] In this embodiment, S502, the convergence analysis of the finite-time backstepping controller is performed using the Lyapunov function, specifically including:

[0175] Two Lyapunov functions are designed using the backstepping method. The first Lyapunov function is designed as follows:

[0176]

[0177] Differentiate V1(t) and combine have to:

[0178]

[0179] in, The error between the first derivative σ2(t) of the sliding surface and the dummy variable α1(t);

[0180] when At that time, there exists Right now Based on this, the second Lyapunov function is designed as follows:

[0181]

[0182] Taking the derivative of V2(t) and substituting it into the designed finite-time backstepping controller, we can obtain:

[0183]

[0184] Convergence time satisfies:

[0185]

[0186] This leads to the finite-time convergence of the finite-time backstepping controller. Therefore, the finite-time anti-interference control method for the omnidirectional pneumatic flexible robotic arm proposed in this scheme is stable and effective.

[0187] In a further preferred embodiment of the present invention, to verify that the finite-time anti-interference control method for a universal pneumatic flexible manipulator proposed in this invention has good control performance, experimental verification is provided to illustrate that the universal pneumatic flexible manipulator has high control accuracy and good anti-interference capability under the control method proposed in this invention, as detailed below:

[0188] The initial position of the omnidirectional pneumatic flexible robotic arm's end effector is set to (0, 0, 67.5). The omnidirectional pneumatic flexible robotic arm is driven by 12 McKibben-type pneumatic artificial muscles. A voltage signal is supplied to the electro-proportional valve via an industrial control computer board configured on the experimental platform. The electro-proportional valve controls the internal air pressure of the pneumatic artificial muscles, causing the omnidirectional pneumatic flexible robotic arm to deflect accordingly. The deflection angle is collected by an angle sensor, and the position of the end effector is obtained through spatial position analysis as the system output.

[0189] The control objective is set as follows:

[0190] Two step signals are used as the desired signals for the two axes of the end effector of the omnidirectional pneumatic flexible robotic arm, with amplitudes of v respectively. 01 =18cm, v 02 =11.25cm;

[0191] When given two different desired position signals for the axes, the position curve output by the omnidirectional pneumatic flexible robotic arm is as follows: Figure 4 As shown in the diagram. The solid lines represent the desired position signals input to the two axes, with amplitudes of 18cm and 11.25cm respectively; the dashed lines represent the actual position outputs of the two axes at the desired positions of 18cm and 11.25cm respectively. Figure 4As can be seen, the actual positions of both axes of the omnidirectional pneumatic flexible robotic arm can accurately and without overshoot track the desired position.

[0192] The desired position signals on the two axes are v 01 =18cm, v 02 When x = 11.25 cm, the estimated value z1(t) of the output position x1(t) by the finite-time extended state observer is as follows: Figure 4 As shown. Where, z 11 (t) represents the output position x of the first axis under the input of the desired position signal at 18cm. 11 The estimated curve of (t); z 12 (t) represents the output position x of the second axis under the input of the desired position signal of 11.25cm. 12 The estimated curve of (t). From Figure 5 It can be seen that when different desired position signals are input to the two axes, the finite-time extended state observer can quickly and stably estimate the actual output position x1(t).

[0193] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments described above, and any obvious improvements, substitutions, or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention.

Claims

1. A finite time anti-disturbance control method for a gimballed pneumatic flexible manipulator, characterized in that, Including the following steps: The DH method is used to simplify the omnidirectional pneumatic flexible manipulator into a linkage model, and kinematic analysis is performed to obtain the kinematic analysis model and the position of the end point of the omnidirectional pneumatic flexible manipulator. Based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator, a dynamic model of the omnidirectional pneumatic flexible manipulator is established using the Euler-Lagrange method. The uncertainty of the omnidirectional pneumatic flexible manipulator is considered as a disturbance, and a second-order mathematical model of the pneumatic flexible manipulator is established. Design a finite-time extended state observer to estimate the disturbance, and design a finite-time backstepping controller based on the disturbance estimate to compensate for the impact of the disturbance on the system; The steps of designing a finite-time extended state observer to estimate the disturbance and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the impact of the disturbance on the system include: The finite-time extended state observer is: In the formula, , and ; , and are positive adjustable parameters, , , is an error variable in the finite-time extended state observer; The finite-time backstepping controller is: wherein is a system parameter; is a positive adjustable parameter; sliding surface is designed as: in, for The first derivative, For the backstepping method, [the variable is] a dummy variable, where [the variable is] a dummy variable. For sliding surface The error between 0 and 0; In the formula, This refers to the positional error of the omnidirectional pneumatic flexible robotic arm. , , , , , , , and A positive adjustable parameter. For the desired position, Obtained by tracking differentiator . 2.The finite time anti-disturbance control method for a gimbaling pneumatic flexible manipulator according to claim 1, wherein The steps of simplifying the omnidirectional pneumatic flexible manipulator into a linkage model using the DH method and performing kinematic analysis to obtain the kinematic analysis model and the position of the end point of the omnidirectional pneumatic flexible manipulator include: Using the DH method, the mechanical structure of the omnidirectional pneumatic flexible manipulator is simplified into a six-bar model. To obtain the position of the end effector of the manipulator, a transition matrix is ​​introduced. ; in, It is the torsion angle of the (i-1)th link; It is the offset distance of the i-th link; It is the angle of the i-th joint; based on the transfer matrix, the transfer matrix of each link of the omnidirectional pneumatic flexible manipulator is obtained as follows: Multiplying the seven transition matrices together, the position of the robotic arm's end effector is obtained as follows: in, In the formula: , , are the coordinates of the end point in the X, Y, Z axes of the spatial coordinate system, , , is the deflection angle of the ith joint, wherein , l is the length of the mechanical arm link. 3.The finite time anti-disturbance control method of a gimbaling pneumatic flexible manipulator according to claim 1, wherein, The steps for establishing the dynamic model of the omnidirectional pneumatic flexible manipulator using the Euler-Lagrange method based on the kinematic analysis model of the omnidirectional pneumatic flexible manipulator include: The Euler-Lagrange equations can be expressed in the following form: Based on the Euler-Lagrange equations and kinematic analysis, the dynamic model of the omnidirectional pneumatic flexible manipulator is expressed as follows: wherein: is the matrix of inertia, is the matrix of Coriolis forces, It is the gravity matrix; It is the mass of the connecting rod; It is the gravitational acceleration matrix; It is the centroid distance matrix; J is the Jacobian matrix, and Q is the parameter matrix; in: These are the three intermediate variables obtained by concatenating the transition matrix A and the constant matrix Q; Based on the driving method of the omnidirectional pneumatic flexible robotic arm, the dynamic model is transformed and each element is written in vector form: In the formula: in, It is a vector representation of the deflection angle. yes The vector representation of , yes The vector representation of , yes The vector representation of , This refers to the proportional coefficient of the electro-proportional valve. For preload voltage, For the original length of the pneumatic artificial muscle, The lever arm is the force arm. The total length of the woven net, The number of wraps around the outer woven mesh. It is the control voltage of the i-th joint, where ; It is an identity matrix. 4.The finite time anti-disturbance control method of a gimbaling pneumatic flexible manipulator according to claim 1, wherein, The steps for establishing a second-order mathematical model of the omnidirectional pneumatic flexible manipulator, considering the uncertainty of the manipulator as a disturbance, include: Combining the kinematic analysis model and the dynamic model, the second-order mathematical model of the omnidirectional pneumatic flexible manipulator is as follows: In the formula, in, yes Each element, yes Each element, yes elements, yes The first-order partial derivative, yes The first-order partial derivative, yes The first derivative, yes The first derivative; Uncertainty regarding the omnidirectional pneumatic flexible robotic arm.

5. The finite-time anti-disturbance control method for a gimbaling pneumatic flexible manipulator according to claim 1, wherein After the steps of designing a finite-time extended state observer to estimate the disturbance and designing a finite-time backstepping controller based on the disturbance estimate to compensate for the impact of the disturbance on the system, the method further includes: performing convergence analysis on the finite-time extended state observer using Lyapunov functions and performing convergence analysis on the finite-time backstepping controller using Lyapunov functions.

6. The finite-time anti-disturbance control method for a gimbaling pneumatic flexible manipulator according to claim 5, wherein The convergence analysis of the finite-time extended state observer using Lyapunov functions specifically includes: We design the Lyapunov equations for a finite-time extended state observer and prove its finite-time convergence. First, we present the error system of the finite-time extended state observer as follows: Design proof required related variables Taking the derivative gives in, The Lyapunov equations are designed as follows: For Lyapunov function equations Differentiate: Bringing into the above formula: , Bringing into the above formula: Convergence time satisfies: in: , are two bounded constants; is the initial value of the Lyapunov function; , , .

7. The finite-time anti-disturbance control method for a gimbaling pneumatic flexible manipulator according to claim 5, wherein The convergence analysis of the finite-time backstepping controller using Lyapunov functions specifically includes: Two Lyapunov functions are designed using the backstepping method. The first Lyapunov function is designed as follows: For derivation and combining we obtain: in, The first derivative of the sliding surface With dummy variables Error between; when At that time, there exists Right now Based on this, the second Lyapunov function is designed as follows: For Taking the derivative and substituting into the designed finite-time backstepping controller, we have Convergence time satisfies: 。

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